Pareto Set Prediction Assisted Bilevel Multi-objective Optimization

TL;DR

This paper introduces PSP-BLEMO, a neural network-assisted method that predicts the Pareto set in bilevel multi-objective optimization, significantly reducing computational costs and improving efficiency over traditional nested search techniques.

Contribution

The paper presents a novel neural network-based approach to predict Pareto sets in bilevel multi-objective problems, enabling more efficient optimization by avoiding nested searches.

Findings

The proposed method is competitive with state-of-the-art techniques.

It reduces the number of function evaluations needed.

Effective on both deceptive and non-deceptive problems.

Abstract

Bilevel optimization problems comprise an upper level optimization task that contains a lower level optimization task as a constraint. While there is a significant and growing literature devoted to solving bilevel problems with single objective at both levels using evolutionary computation, there is relatively scarce work done to address problems with multiple objectives (BLMOP) at both levels. For black-box BLMOPs, the existing evolutionary techniques typically utilize nested search, which in its native form consumes large number of function evaluations. In this work, we propose to reduce this expense by predicting the lower level Pareto set for a candidate upper level solution directly, instead of conducting an optimization from scratch. Such a prediction is significantly challenging for BLMOPs as it involves one-to-many mapping scenario. We resolve this bottleneck by supplementing the dataset using a helper variable and construct a neural network, which can then be trained to map the variables in a meaningful manner. Then, we embed this initialization within a bilevel optimization framework, termed Pareto set prediction assisted evolutionary bilevel multi-objective optimization (PSP-BLEMO). Systematic experiments with existing state-of-the-art methods are presented to demonstrate its benefit. The experiments show that the proposed approach is competitive across a range of problems, including both deceptive and non-deceptive problems